Preheat oven to 450 degrees F. Place peppers into a 13x9-inch baking dish. Sprinkle with ½ teaspoon fresh rosemary (or ¼ teaspoon dried), salt, and black pepper to taste. Roast 20 minutes, stirring once. Meanwhile, sprinkle the 4 chicken breast halves with salt, pepper, and 1 teaspoon fresh rosemary (or ½ teaspoon dried).
Remove the peppers from the oven, stir, and tuck the chicken and garlic between the pepper pieces. Reduce oven temperature to 400 degrees F. Roast, turning the chicken and rearranging the peppers and garlic once or twice, until chicken is cooked through but still juicy, and peppers are well done, 35 to 40 minutes.